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A short electric dipole is placed at the origin with its dipole moment vector p = p₀ i . The electric field vector at a point with position vector r ₁ = a i is E ₁ . The electric field vector at a point with position vector r ₂ = 2a j is E ₂ . Which of the following correctly expresses E ₂ in terms of E ₁ ?

Options

  1. AE ₁ 16
  2. B- E ₁ 16
  3. C- E ₁ 8
  4. DE ₁ 8

Correct answer

B. - E ₁ 16

Step-by-step solution

The point with position vector r ₁ = a i lies on the axial line of the dipole. The electric field at this point is given by: E ₁ = 1 4 ₀ 2p₀ a^3 i The point with position vector r ₂ = 2a j lies on the equatorial line of the dipole. The electric field at an equatorial point is antiparallel to the dipole moment. Its value is: E ₂ = - 1 4 ₀ p₀ (2a)^3 i = - 1 4 ₀ p₀ 8a^3 i From the expression for E ₁ , we have 1 4 ₀ p₀ a^3 i = E ₁ 2 . Substituting this into the expression for E ₂ gives: E ₂ = - 1 8 ( E ₁ 2 ) = - E ₁ 16

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